As well known, non-Hermitian Hamiltonians such as (REF ) need a suitable modification of the scalar product and resolution of identity [1]}, [2]}, [3]}, [4]}. A new scalar product can be defined as
\(\langle \langle \Psi | \Phi \rangle \rangle = \int (P_2 T \Psi ) \Phi d{\bf x}, \) 
